On the Distributions of the State Sizes of Discrete Time Homogeneous Markov Systems



The evolution of a closed discrete-time homogeneous Markov system (HMS) is determined by the evolution of its state sizes in time. In order to examine the variability of the state sizes, their moments are evaluated for any time point, and recursive formulae for their computation are derived. As a consequence the asymptotic values of the moments for a convergent HMS can be evaluated. The respective recursive formula for a HMS with periodic transition matrix is given. The p.d.f.’s of the state sizes follow directly by means of the moments. The theoretical results are illustrated by a numerical example.


Stochastic population systems Discrete-time homogeneous Markov models Markov systems 

AMS 2000 Subject Classification

Primary 90B70 62E99; Secondary 91D35 


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsAristotle University of ThessalonikiThessalonikiGreece

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